Solve x-5/4>5x+1/6-1

$$\frac{ x-5 }{ 4 } > \frac{ 5x+1 }{ 6 } -1$$

Solve for x

$$x<-\frac{5}{7}$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 4,6. Since 12 is positive, the inequality direction remains the same.

$$3\left(x-5\right)>2\left(5x+1\right)-12$$

Use the distributive property to multiply 3 by x-5.

$$3x-15>2\left(5x+1\right)-12$$

Use the distributive property to multiply 2 by 5x+1.

$$3x-15>10x+2-12$$

Subtract 12 from 2 to get -10.

$$3x-15>10x-10$$

Subtract 10x from both sides.

$$3x-15-10x>-10$$

Combine 3x and -10x to get -7x.

$$-7x-15>-10$$

Add 15 to both sides.

$$-7x>-10+15$$

Add -10 and 15 to get 5.

$$-7x>5$$

Divide both sides by -7. Since -7 is negative, the inequality direction is changed.

$$x<-\frac{5}{7}$$